The price of a stock is 40 The price of a oneyear European p

The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a one-year European call option on the stock with a strike price of $50 is quoted as $5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options. Draw a diagram illustrating how the investor’s profit or loss varies with the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?

Suppose that you are the manager and sole owner of a highly leveraged company. All the debt will mature in one year. If at that time the value of the company is greater than the face value of the debt, you will pay off the debt. If the value of the company is less than the face value of the debt, you will declare bankruptcy and the debt holders will own the company.

Express your position as an option on the value of the company.

Express the position of the debt holders in terms of options on the value of the company.

What can you do to increase the value of your position?

Solution

ANSWER.

The investor’s profit varies with the stock price in the first case.

Loss $ 1,200 will get if stock price is less than $30.

As the stock price increases from $30 to $50 the profit increases from –$1,200 to $800.

Above $50, the profit is $800.

call which is $10 out of the money is less expensive than a put which is $10 out of the money.

The profit varies with stock price in the second case.

In this case the profit pattern has a zigzag shape.

many different patterns can be obtained by including calls, puts, and the underlying asset in a portfolio.